Need help with sir model method question

A new disease is circulating small town population 10,100 and evolves according to SIR equations

S’=-aSI
I’= aSI-bI
R’= bI

It appears that the disease lasts about an average of 20 days. It is also thought that initially, there were 100 people. That is initially we had

S(0)= 10,000
I(0) =100
R(0) =0

One day later, we had 8 newly people infected.


a) find the transmission and recovery coefficients a and b

b) using triangle t=2, find estimates for S(4), I(4), R(4)

c) find threshold value for number of susceptibles. What does the value found mean?